1. Field of the Invention
The present invention relates to a circuit/electromagnetic field analysis method obtaining a current/voltage value and electromagnetic field intensity, implemented by coupling an electromagnetic field analysis method and circuit analysis method together.
2. Description of the Background Art
There is conventionally known a circuit/electromagnetic field analysis method implemented by coupling together a finite difference time domain method of differentiating Maxwell's differential equation for solving in a time domain (hereinafter, referred to as “FDTD method”) and a circuit analysis method as typified by SPICE (Simulation Program with Integrated Circuit Emphasis: built by The University of California, Berkeley), for example, to obtain a current/voltage value and electromagnetic field intensity.
In the past, various schemes have been disclosed as a simulation method of an electromagnetic wave emitted from an electronic device such as the FDTD method introduced in Finite Difference Time Domain Method for Electromagnetic Field and Antenna, 1st ed., 1998, by Toru Uno, CORONA PUBLISHING CO., LTD.
FIG. 12 is a diagram to describe analytical cells in the FDTD method.
The FDTD method will be briefly described with reference to FIG. 12. The FDTD method employs an analytical domain that includes components such as a printed circuit board and cavity of an electronic device as well as the ambient space. The analytical domain is divided into small cuboids called cells, as shown in FIG. 12. At this stage, the permeability, permittivity and conductivity depending on the substance constituting the cell are applied to each cell. As used herein, the length of each side of the cell in the x, y and z directions are set as Δx, Δy and Δz, respectively.
Then, respective x, y and z components of either the electric field intensity E or magnetic field intensity H that are vector quantities, for example, (Ex, Ey, Ez) of the electric field intensity, are arranged on each side of the cell lattice, whereas respective components of x, y and z of the other magnetic field intensity, for example, (Hx, Hy, Hz) are arranged at the center of the lattice plane of the cell, perpendicular to the lattice plane.
By employing the central difference for the time and space in the differential Maxwell's equation, the following two expressions are given:
                              E          n                =                                                            1                -                                                      σΔ                    ⁢                                                                                  ⁢                    t                                                        2                    ⁢                    ɛ                                                                              1                +                                                      σΔ                    ⁢                                                                                  ⁢                    t                                                        2                    ⁢                    ɛ                                                                        ⁢                          E                              n                -                1                                              +                                                                      Δ                  ⁢                                                                          ⁢                  t                                ɛ                                            1                +                                                      σΔ                    ⁢                                                                                  ⁢                    t                                                        2                    ⁢                    ɛ                                                                        ⁢                          ∇                              ×                                  H                                      n                    -                                          1                      2                                                                                                                              Expression        ⁢                                  ⁢                  (          1          )                                                  H                      n            +                          1              2                                      =                              H                          n              -                              1                2                                              -                                                    Δ                ⁢                                                                  ⁢                t                            μ                        ⁢                          ∇                              ×                                  E                  n                                                                                        Expression        ⁢                                  ⁢                  (          2          )                    where σ, ∈ and μ represent the conductivity, permittivity and permeability, respectively, and Δtem represents the time step in calculation.
The procedure of obtaining the electric field intensity and magnetic field intensity corresponding to time elapse in the FDTD method will be described hereinafter.
With Δtem as the time step width, it is assumed that the electric field intensity En−1 at time (n−1) Δtem and the magnetic field intensity Hn−1/2 at time (n−½) Δtem are given. The electric field intensity En−1 at time nΔtem is calculated by assigning En−t and Hn−1/2 to Expression (1). For the magnetic field intensity, Hn+1/2 is calculated by assigning En and Hn−1/2 to Expression (2) at time (n+½)Δtem. Thus, electric field intensity E and magnetic field intensity H are calculated alternately in time in the FDTD method.
At this stage, the time step width Δtem in the FDTD method must satisfy the Courant stability condition shown in Expression (3) with respect to the cell size.
                              Δ          ⁢                                          ⁢                      t            em                          ≤                  1                      c            ⁢                                                                                (                                          1                                              Δ                        ⁢                                                                                                  ⁢                        x                                                              )                                    2                                +                                                      (                                          1                                              Δ                        ⁢                                                                                                  ⁢                        y                                                              )                                    2                                +                                                      (                                          1                                              Δ                        ⁢                                                                                                  ⁢                        z                                                              )                                    2                                                                                        Expression        ⁢                                  ⁢                  (          9          )                    where c is the light velocity. It is generally known that the calculated value will be diffused if Expression (3) is not satisfied for time step width Δtem.
Since the FDTD method is an analysis method of a closed domain, there is a drawback that reflectance will occur at the outer wall of the analytical domain when an open domain problem is handled. In view of this drawback, a virtual boundary called an absorption boundary must be provided to avoid reflectance at the outer wall of the analytical domain. In the aforementioned Finite Difference Time Domain Method for Electromagnetic Field and Antenna, various proposals for absorption boundary conditions are introduced.
As a tool for analyzing the transient state of an electrical circuit including a non-linear element, a circuit simulator as typified by SPICE is generally employed. Moreover, libraries covering a great amount of subcircuits including integrated circuits are provided by manufacturers, software companies, academia parties, and the like.
The analysis method in a circuit simulator of SPICE and the like will be briefly described. First, a non-linear simultaneous differential equation is derived by applying a modified nodal analysis method to a net list in which are described the connection information between circuit elements and parameters of the circuit elements with the current/voltage value at the nodes of the circuit that is the target of analysis as variables. This non-linear simultaneous differential equation is converted into an algebraic equation employing the difference in the time domain and Newton's iteration method. By solving this algebraic equation, the circuit current/voltage value at the analysis time can be obtained. Then, the analysis time is stepped up by just the difference in the time domain. By repeating the computation set forth above, the transient state of the circuit voltage/current is worked out.
The aforementioned Finite Difference Time Domain Method for Electromagnetic Field and Antenna and Japanese Patent Laying-Open No. 11-153634 disclose an analysis method implemented by coupling the aforementioned FDTD method and circuit simulator such as SPICE together in a time domain to analyze the electromagnetic field intensity and circuit transient response of an analytical domain including a non-linear circuit element.
FIG. 13 is a conceptual diagram representing the coupling of the FDTD method with a circuit simulator.
In the aforementioned Finite Difference Time Domain Method for Electromagnetic Field and Antenna, a hybrid method based on an equivalent current source method and equivalent voltage source method is described. The equivalent current source method will be described here. It is assumed that ports provided across the two terminals of an element that is to be analyzed by a circuit simulator are present in one cell parallel to the z-axis. Ampere's law represented in Expression (4) can be rewritten as Expression (5) for an FDTD cell including an element port.
                                          ɛ            ⁢                                          ⅆ                E                                            ⅆ                t                                              +                      J            ⁡                          (              E              )                                      =                  ∇                      ×            H                                              Expression        ⁢                                  ⁢                  (          4          )                                                              C            ⁢                                          ⅆ                V                                            ⅆ                t                                              +                      I            ⁡                          (              V              )                                      =        I                            Expression        ⁢                                  ⁢                  (          5          )                    
As used herein, V is the voltage applied to the chip, C=∈A/Δz is the electrostatic capacitance of the FDTD cell (A=Δx·Δy is the area and Δz is the height of the FDTD cell), I(V)(=A·J(E)) is the current flowing through the port, and I is the total cell current A·∇×H.
Namely, the coupling of the FDTD method and circuit simulator is represented by an equivalent circuit such as a capacitor C, a constant current source I, and elements, connected in parallel.
FIG. 14 is a conceptual diagram of the data flow in the FDTD method and circuit simulator over time.
Data transfer between the FDTD method and circuit simulator in the equivalent current source method will be described with reference to FIG. 14.
It is assumed that electric field intensity En−1 at time (n−1) Δtem and magnetic field intensity Hn−3/2 at time (n− 3/2) Δtem are given. Magnetic field intensity Hn−1/2 at time (n−½) Δtem is obtained by assigning En−1 and Hn−3/2 to Expression (2).
It is to be noted that the method of calculating electric field intensity En at time nΔtem differs between a cell that includes an element and a cell that does not include an element. With regards to the cell that does not include the element, electric field intensity En can be obtained by assigning En−1 and Hn−1/2 into Expression (1). With regards to the cell that includes the element, electric field intensity En is calculated by a circuit analysis through a circuit simulator.
In the equivalent circuit of FIG. 13, circuit simulation is performed with a sufficiently fine time step width from time (n−1) Δtem to time nΔtem on condition Vn−1=Ezn−Δz as the initial voltage value of the capacitor, and a constant value I=A·∇×Hn−1/2 as the equivalent current source. The element voltage value Vn at time nΔtem is converted into electric field intensity Ezn=Vn/Δz of the cell including an element, and passed over to the FDTD method.
Similarly in the equivalent voltage source method, analysis is carried out including the steps of obtaining the equivalent voltage source value from the electric field obtained by the FDTD method, analyzing through a circuit simulator, the current value at the time of obtaining the magnetic field by the FDTD method, converting the result into a magnetic field value, and passing over the same to the FDTD method.
Thus, analysis is carried out with the electromagnetic field intensity by the FDTD method and the current/voltage value by the circuit simulator set in correspondence in the hybrid method.
Moreover, Japanese Patent Laying-Open No. 11-153634 proposes a method for realizing data transfer between the FDTD method and circuit simulator when the aforementioned hybrid method employs time steps that can be increased and decreased in a circuit simulator.
FIGS. 15A and 15B represent equivalent circuits of items.
For an equivalent circuit of a 2-terminal item, a circuit/electromagnetic field coupling analysis implemented by coupling circuit analysis and electromagnetic field analysis together can be carried out by setting one port between the circuit analysis and electromagnetic field analysis, as set forth above. Furthermore, by setting two or more ports even in an equivalent circuit of an item having three or more terminals as shown in FIG. 15A, a circuit/electromagnetic field coupling analysis can be carried out similarly as a circuit as shown in FIG. 15B.
According to the method set forth above, a coupling analysis of analyzing at the same time the electromagnetic field distribution in one electromagnetic field analysis space, and the current and voltage of a circuit item present thereon can be realized by coupling the FDTD method and circuit simulator together.
FIG. 16 is a conceptual diagram of the configuration of a general electronic device product, viewed from the side.
A general electronic device product is often based on a configuration in which the internal circuit required for the operation of the product is allotted to a plurality of substrates that are connected through cables. In such a configuration, the signal quality and/or noise radiation at the lines of signals running over the two substrates and the cables establishing connection therebetween often becomes an issue. Accordingly, there is a need to perform a simulation on such signal lines.
FIG. 17 is a conceptual diagram to describe a circuit simulation with respect to the electronic device product shown in FIG. 16.
Consider the case of performing a simulation on the cable (signal line) as shown in FIG. 16, using the technique disclosed in the aforementioned Finite Difference Time Domain Method for Electromagnetic Field and Antenna and Japanese Patent Laying-Open No. 11-153634. Since it is necessary to dispose two substrates within the same electromagnetic field analytical domain, as shown in FIG. 17, electromagnetic field analysis has to be carried out for the space between the substrates even in the case where the mutual electromagnetic field effect between the substrates through space excluding the cable is considered to be small. Further, because of the same electromagnetic field analysis space, an analysis of the entire space must be carried out with a cell size and time step corresponding to the smaller substrate even in the case where the fineness of the substrates differ from each other. Therefore, more computation resource than needed will be consumed during the analysis calculation.